Luis is 8 years older than William. Six years ago, Luis was 3 times as old as William. How old is William now?
Explanation: We can use the given information to write down two equations that describe the ages of Luis and William. Let Luis's current age be $l$ and William's current age be $w$ The information in the first sentence can be expressed in the following equation: $l = w + 8$ Six years ago, Luis was $l - 6$ years old, and William was $w - 6$ years old. The information in the second sentence can be expressed in the following equation: $l - 6 = 3(w - 6)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $w$ , it might be easiest to use our first equation for $l$ and substitute it into our second equation. Our first equation is: $l = w + 8$ . Substituting this into our second equation, we get the equation: $(w + 8)$ $-$ $6 = 3(w - 6)$ which combines the information about $w$ from both of our original equations. Simplifying both sides of this equation, we get: $w + 2 = 3 w - 18$ Solving for $w$ , we get: $2 w = 20$ $w = 10$.